Comma outside a quotation mark

The comma should be inside the quotation marks in both British and American English in that sentence.

Is is the rule?

I often read in books that in British English comma is put outside the quotation mark in a sentence like the above.

For example, I found the following examples:

1. "I'll go", she said.
2. "Come here", he told me.

What about a sentence like the following?

Her behaviour was "totally unacceptable", according to Mr Jones.

Could you tell me please what rule I should follow in British English?

(Here I do not quote the whole sentence)

I'm sorry I had to correct my post:

Is is the rule?

I often read in books that in British English comma is put outside the quotation mark in a sentence like the above.

For example, I found the following examples:

1. "I'll go", she said.
2. "Come here", he told me.

What about a sentence like the following?

Her behaviour was "totally unacceptable", according to Mr Jones.
(Here I do not quote the whole sentence)

Could you tell me please what rule I should follow in British English?